Take a stick of unit length and break it into two pieces, choosing the
break point at random. Now break the longer of the two pieces at a
random point. What is the probability that the three pieces can be
used to form a triangle?

In the sample space for a probability experiment, outcome A is twice as
likely as outcome B. Outcome C is two-thirds as likely as outcome B.
Outcome C is twice as likely as outcome D. Find the probability of each
outcome in the sample space.

Given a set S = {A_1, A_2, A_3, ..., A_N}, a probability student struggles to enumerate
all cases of random samples of size k that contain at least its first two elements, A_1
and A_2. Doctor Schwa provides hints based on complementary probability and the
principle of inclusion and exclusion.

I read that if 25 students take a 10-question true or false test and
they all randomly guess at the answers, there is a 75% chance that at
least one of them will score 80% or better. How is that possible? It
seems too high to me.